Simple question, tricky answer.
According to the US census, 1,754,331 citizens ages 25 and up have doctorates.
This Answer.com Answer states that roughly 1% of Americans ages 25 and up have research doctorates and that, if we were to include “people with professional degrees who are normally referred to with Dr title like physicians, dentists, etc (MD, DDS, etc)”, the number would rise to approximately 2.95%. What the answerer did was add the “doctorate” row and the “professional degree” row together, yielding 5,373,866 or approximately 2.95% of the total US population over the age of 25. The problem with this is that a professional degree is not necessarily a professional doctorate. There are numerous professional masters degrees. I have one - a masters in library and information science. Further, it does not appear that the census table the answer cites differentiates between research doctorates (PhD, EdD, etc) and professional doctorates (MD, PsyD, etc). So the 1.75 million is for any American 25 years and older with any kind of doctorate.
This Wisegeek article (which offers statistics, but does not cite its sources), states that there are 884,974 physicians in the United States, or .48% of the population (Wisegeek says .29%, but using the 182,211,639 figure for Americans 25 years and older, it works out to .48%. It’s possible that the Wisegeek figure includes all Americans or Americans 18 and up.) Subtract that figure from the initial 1% and we get .52% for non-MD doctorate holders. Of course, some doctorate holders have non-PhD, non-MD doctorates…
Another place to look for the information would be the Bureau of Labor Statistics, which states that there are approximately 1.7 million postsecondary teachers in the United States. Going back to the US census, which tells us that there are 182,211,639 US citizens over the age of 25, 1.7 million works out to be about .93%. Of course, not all postsecondary teachers have PhDs - some are graduate student TAs still working on their doctorates, some have MDs (med school professors) or other professional doctorates, and some fields simply do not require the PhD (dance, law, engineering, etc). This information also fails to account for PhD holders who do not work in academia.
So the question is definitely trickier than it would initially appear. There does not seem to be an easily-accessed definitive answer. However, using the information above, I am comfortable estimating that .25 to .50% of the US population ages 25 and older have PhDs.